Is the One-time Pad truly unbreakable? Yes and no. You can brute force it and decrypt the message for every possible key of the same length as the message. But you are then left with every possible message that is of the same length. Which one is the real one? There is no way to tell. Even if you know a word that will be in the message and even if you know exactly where it is in the message then you are still left with every possible message that has that word in that place. You really haven't learned anything, because you already knew that word. So it is effectively unbreakable because of all the possible false decryptions.

"Wow", you say, "then why doesn't everybody use it?" There are many problems related to the One-time Pad. It suffers from problems of key generation, key distribution, and insuring keys are not reused. First you have to generate a key of random letters (or whatever is in the cipher alphabet) that is at least the length of the message to be decrypted. This is an expensive process and true random-ness is difficult to obtain. Next you have to get everybody that needs to decrypt your messages the keys and you have to make sure everybody is using the same key at the same time. Finally you have to make sure keys are never reused. Because if you reuse a key you've made the codebreakers job much easier.

Most implementation of a One-Time Pad in computers use XOR on the bits instead of the Vigenère Square on the characters. The same principles still apply because I think the Vigenère Square works as a sort of alphabetical XOR. For another version, which was used during WWII, see One Time Pad.

and so on. Each number is then used as the base for an alphabet. For example, the word THAT could be enciphered like this:

THAT written as numbers is 20 7 1 20.

I then look at the first 4 numbers on my pad, and add them to my message.

053 + 20 = 73
786 + 7 = 793
423 + 1 = 424
156 + 20 = 176

To complicate things we sometimes use non-carrying addition. We also might place a different letter as the base of the alphabet. So, instead of 053 equaling the first letter, A, it might equal J. Thus, if A was enciphered we would take away 10 to compensate for the J. We use Cyrillic, of course, but this example in your Latin script is probably easier to understand. Because each alphabet is completely random, there is literally no way to break this system (outside of having the codebook and knowing when each pad was used).

Suppose you have a really important secret that you need to transmit. Say, you want to plan a surprise party for one of your friends, but you know she has
a working quantum computer in her basement and routinely intercepts your mail.
Are you going to entrust the security of your invitations to the simple factoring of large primes? No, of course not. In extreme cases like this, standard public key
cryptography just doesn't cut it. You need the unbreakable (or at least as unbreakable as your random is random) reliability and utter inconvenience of the one time pad!

But this isn't like the old days I hear you complain, I have a lot of super-sensitive data to transmit. Far too much to sit there encrypting and decrypting it by hand! Don't worry, I've got you covered. As chkno points out in kid sister encryption, every lame-ass cipher-kiddie eventually writes what they think is a slick XOR encryption tool. Here's mine. I'll even give you:

Unplug your new one time pad generation station from the network. Do it. Do it now. No ethernet, no modem, hell, if you can manage it get that sucker off the power grid. Consider moving to an underground bunker before you continue. This is about absolute paranoia, dagnabit. Everyone wants a piece of your data, and all hard-lines are suspect. If you got a throw-away computer with wireless, I hate you.

Put the CDs in separate sealed envelopes. (No, no, seal them after you put the CDs in them...) Consider lining the envelopes with tin foil or something. If space aliens can read your mind, they can certainly read your optical media.

Smash the computer to bits. Be thorough. Destroy every last chip. Grind it to dust, and scatter it in several different places.

Keep one of the sealed CDs for yourself, and at a carefully arranged and concealed meeting, give the other to the friend you want to securely communicate with.

Copy the pad file to the computer, and destroy the CD. Be as thorough as when you destroyed that last computer.

Using the perl script below (which you thoughtfully copied to the computer before unplugging it), XOR the data you want to send with the pad file. Mmm, crypty.

Burn the new XORed file to another CD, and once again destroy the computer.

Send the XORed file to your friend. Be as careless as you like here! E-mail it, fedex it, publish it in the newspaper, drop leaflets from the sky, etc. As long as you followed all the other steps carefully, this data is utterly useless to everyone but your friend. Take that, your many enemies!